{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:SQ5WYJBVV5IPNLVHH3PWWNQ4DY","short_pith_number":"pith:SQ5WYJBV","canonical_record":{"source":{"id":"1904.10585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-24T00:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"98ae7e8a73d0b398960bde018262ea2ef24984cb87e0068365b55ad68304f65a","abstract_canon_sha256":"86a8c4021516f2b7699120ca9b106b225b4146e3ed1387fe9fa5ca5562d019d0"},"schema_version":"1.0"},"canonical_sha256":"943b6c2435af50f6aea73edf6b361c1e3c33ce9403466cfaf5e91827fdf012b4","source":{"kind":"arxiv","id":"1904.10585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10585","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10585v1","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10585","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"SQ5WYJBVV5IP","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SQ5WYJBVV5IPNLVH","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SQ5WYJBV","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:SQ5WYJBVV5IPNLVHH3PWWNQ4DY","target":"record","payload":{"canonical_record":{"source":{"id":"1904.10585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-24T00:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"98ae7e8a73d0b398960bde018262ea2ef24984cb87e0068365b55ad68304f65a","abstract_canon_sha256":"86a8c4021516f2b7699120ca9b106b225b4146e3ed1387fe9fa5ca5562d019d0"},"schema_version":"1.0"},"canonical_sha256":"943b6c2435af50f6aea73edf6b361c1e3c33ce9403466cfaf5e91827fdf012b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:53.327733Z","signature_b64":"yhQndgYB1PKUb5N5QQ7BNHpDE5ufCXmpeHEFPK9ACWL8ZiZo4ij/yGkxgRnsueWfMMt2AUkT2r4IHvwHBvSeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"943b6c2435af50f6aea73edf6b361c1e3c33ce9403466cfaf5e91827fdf012b4","last_reissued_at":"2026-05-17T23:47:53.327276Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:53.327276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.10585","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U90ETwn9WsSIL7PQ1KEGrLHE0j2TN/31mmyMruPTLyR/7R9aWhBFpDuYlRPh44aALVNW0RE3fUbzNaeIyecXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:07:22.090015Z"},"content_sha256":"4446d99aebed2f8b7c5c32fd3c0194749ea637485783f2fb6795382c6d9a1bc8","schema_version":"1.0","event_id":"sha256:4446d99aebed2f8b7c5c32fd3c0194749ea637485783f2fb6795382c6d9a1bc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:SQ5WYJBVV5IPNLVHH3PWWNQ4DY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low-rank Matrix Optimization Using Polynomial-filtered Subspace Extraction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Haoyang Liu, Yaxiang Yuan, Yongfeng Li, Zaiwen Wen","submitted_at":"2019-04-24T00:40:32Z","abstract_excerpt":"In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at each iteration which takes most of the computation time. In order to reduce the cost, we propose an inexact algorithm framework based on a polynomial subspace extraction. The idea is to use an additional polynomial-filtered iteration to extract an approximated eigenspace, and project the iteration matrix on this subspace, followed by an optimization update. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10585","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UXi1XpG+GwIc+TxboqAjdnnuGUPhpVsP/7zYXThEtW08FErsl3/ZdKSzlBOnGA0AhyYsSZDa6xj58f2yyy0sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:07:22.090393Z"},"content_sha256":"ea967874b9ea18ad9750e1297eac19bf090b1e3bdb8160a946091415ae0e9f7a","schema_version":"1.0","event_id":"sha256:ea967874b9ea18ad9750e1297eac19bf090b1e3bdb8160a946091415ae0e9f7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQ5WYJBVV5IPNLVHH3PWWNQ4DY/bundle.json","state_url":"https://pith.science/pith/SQ5WYJBVV5IPNLVHH3PWWNQ4DY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQ5WYJBVV5IPNLVHH3PWWNQ4DY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T17:07:22Z","links":{"resolver":"https://pith.science/pith/SQ5WYJBVV5IPNLVHH3PWWNQ4DY","bundle":"https://pith.science/pith/SQ5WYJBVV5IPNLVHH3PWWNQ4DY/bundle.json","state":"https://pith.science/pith/SQ5WYJBVV5IPNLVHH3PWWNQ4DY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQ5WYJBVV5IPNLVHH3PWWNQ4DY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SQ5WYJBVV5IPNLVHH3PWWNQ4DY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"86a8c4021516f2b7699120ca9b106b225b4146e3ed1387fe9fa5ca5562d019d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-24T00:40:32Z","title_canon_sha256":"98ae7e8a73d0b398960bde018262ea2ef24984cb87e0068365b55ad68304f65a"},"schema_version":"1.0","source":{"id":"1904.10585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.10585","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1904.10585v1","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.10585","created_at":"2026-05-17T23:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"SQ5WYJBVV5IP","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SQ5WYJBVV5IPNLVH","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SQ5WYJBV","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:ea967874b9ea18ad9750e1297eac19bf090b1e3bdb8160a946091415ae0e9f7a","target":"graph","created_at":"2026-05-17T23:47:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at each iteration which takes most of the computation time. In order to reduce the cost, we propose an inexact algorithm framework based on a polynomial subspace extraction. The idea is to use an additional polynomial-filtered iteration to extract an approximated eigenspace, and project the iteration matrix on this subspace, followed by an optimization update. Th","authors_text":"Haoyang Liu, Yaxiang Yuan, Yongfeng Li, Zaiwen Wen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-24T00:40:32Z","title":"Low-rank Matrix Optimization Using Polynomial-filtered Subspace Extraction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.10585","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4446d99aebed2f8b7c5c32fd3c0194749ea637485783f2fb6795382c6d9a1bc8","target":"record","created_at":"2026-05-17T23:47:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"86a8c4021516f2b7699120ca9b106b225b4146e3ed1387fe9fa5ca5562d019d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-24T00:40:32Z","title_canon_sha256":"98ae7e8a73d0b398960bde018262ea2ef24984cb87e0068365b55ad68304f65a"},"schema_version":"1.0","source":{"id":"1904.10585","kind":"arxiv","version":1}},"canonical_sha256":"943b6c2435af50f6aea73edf6b361c1e3c33ce9403466cfaf5e91827fdf012b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"943b6c2435af50f6aea73edf6b361c1e3c33ce9403466cfaf5e91827fdf012b4","first_computed_at":"2026-05-17T23:47:53.327276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:53.327276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yhQndgYB1PKUb5N5QQ7BNHpDE5ufCXmpeHEFPK9ACWL8ZiZo4ij/yGkxgRnsueWfMMt2AUkT2r4IHvwHBvSeBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:53.327733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.10585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4446d99aebed2f8b7c5c32fd3c0194749ea637485783f2fb6795382c6d9a1bc8","sha256:ea967874b9ea18ad9750e1297eac19bf090b1e3bdb8160a946091415ae0e9f7a"],"state_sha256":"58d61d3b64ab6cbd573a38430f8ffc971512f019f989086c11c95ba767f8f911"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6HLFa7MJCx9Mlzoo7u7JrLYR4EIcA3BhpXmNmTRzMJUKlMSf5Qo47x6Xurv1T3bSkHUJLzG5jKsHCKJzw3u5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:07:22.092512Z","bundle_sha256":"b7d901ca5332585dc12a530d4e558428e74ab878c2aa5d2f6188cb92e3d86369"}}